Unified expressions of ASEP over Málaga (M) turbulence channel

In this paper, we present the unified closed-form expressions of average symbol error probability (ASEP) for both types of system (i.e. coherent and incoherent system) in the presence of pointing error over Málaga (M) turbulence channel. With the help of the approximation of exponential-type presentation of Q-function, the unified closed-form expressions are presented, which are generic enough to encompass almost all the modulation techniques of which ASEP involves the integral power of Q-function. Then, we capitalize on the results to provide the asymptotic expressions at high signal-to-noise ratio (SNR). Additionally, the diversity order and coding gain are presented, which reveal that the diversity order is depended on the channel condition and detection scheme, while the coding gain is relevant to the modulation techniques. Moreover, some special cases are presented, such as the results under Gamma-Gamma distribution and K-distribution. Numerical results corroborate the accuracy of the closed-form expressions for different modulation techniques under different turbulence conditions.